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Consider a pendulum with a flexible connecting rod. When initializing the free motion, the bob would be released at a position such that the connecting rod is flexed as shown in the figure. There are two coupled motions of interest, one being that of the bob and the other being the vibration of the connecting rod. Will the frequency of oscillation of the pendulum and connecting rod synchronize over several oscillations of the pendulum ?

The question suggests a conjecture based on Strogatz's talk which discusses synchrony in nature.

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  • $\begingroup$ Over several oscillations of the pendulum will the frequency of oscillation of the pendulum and connecting rod synchronize? What have you tried that makes you think that? $\endgroup$
    – Gert
    Commented Mar 3, 2021 at 21:26
  • $\begingroup$ It is a conjecture based on Strogatz's talk and the fact that the frequencies are $f_{pend} \propto \sqrt{\frac{l}{g}}$ and $f_{rod} \propto \sqrt{\frac{1}{l}}$. $\endgroup$
    – kbakshi314
    Commented Mar 3, 2021 at 22:06
  • $\begingroup$ I see. Thank you. $\endgroup$
    – Gert
    Commented Mar 3, 2021 at 22:10
  • $\begingroup$ How did you obtain the relation $f_{rod} = \sqrt{\frac{1}{l}}$? $\endgroup$
    – ytlu
    Commented Mar 4, 2021 at 3:44
  • $\begingroup$ I apologize, I meant $f_{rod} \propto \frac{1}{L}$ based on a simplistic model of a string vibrating with fixed ends. $\endgroup$
    – kbakshi314
    Commented Mar 4, 2021 at 18:42

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